A shape consists of a quarter circle (radius r = 4cm) attached to a triangle (side length = 4cm and hypotenuse = 5cm). This shape is surrounded by a square (side length 8cm). If the shape is coloured in, what is the area in the square that is uncoloured?
Draw out what the question says. Geometric problems are easier to solve when they can be visualised. First calculate the area of the quarter circle: A = 1/4 \pi r^2Use Pythagoras to calculate the base length of the triangle. Base length found to be 3cm. Area of a triangle = 1/2 base multiplied by height. Therefore Area = 6cm^2. Area of the enclosing square is 64cm^2.Subtract the area of the triangle and quarter sphere from the square.
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